Question

a^3-b^3 please send me formula method

Answer 1

Proof of  

a³ – b³ = (a – b)(a² + ab + b²)  

you know that  

(a – b)³ = a³ + 3ab(a – b) – b³  

then a³ – b³ = (a – b)³ + 3ab(a – b)  

= (a – b)[(a – b)² + 3ab]  

= (a – b)(a² – 2ab + b² + 3ab)  

= (a – b)(a² + ab + b² )

Answer 2

a³ - b³

= (a - b)³ + 3ab (a - b)

= [(a - b) (a - b)² + 3ab (a - b)]

= (a - b) [(a - b)² + 3ab]

= (a - b) (a² - 2ab + b² + 3ab)

= (a - b) (a² + ab + b²)

$\therefore{}$ a³ - b³ = $\boxed{(a \: - \: b)(a^2 \: + \: ab \: + \: b^2)}$